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प्रश्न
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream is 5 hours. Fid the speed of the stream
उत्तर
Speed of the boat in still water =8 km/ hr.
Let the speed of the stream be x km/hr.
∴Speed upstream=`(8-x)`km/hr.
Speed downstream =`(8+x)` km/hr.
Time taken to go 22 km downstream=`22/(8+x) hr`
Time taken to go 15 km upstream=`15/((8-x))hr`
According to the question:
⇒`22/(8+x)+15/(8-x)=5`
⇒`22/(8+x)+15/(8-x)-5=0`
⇒`(22(8-x)+15(8+x)-5(8-x)(8+x))/((8-x)(8+x))=0`
⇒`176-22x+120+15x-320+5x^2=0`
⇒`5x^2-7x-24=0`
⇒`5x^2-(15-8)x-24=0`
⇒`5x^2-15x+8x-24=0`
⇒`5x(x-3)-8(x-3)=0`
⇒`(x-3) (5x-8)=0`
⇒`x-3=0 or 5x-8=0`
⇒`x=3 or x=8/5`
⇒`x=3` ( ∴Speed cannot be a fraction)
∴Speed of the stream =3 km/ hr
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